Simplify the given expression into the form a+bi, where a and b are rational numbers.
2(-36 - 3i) +(5 +2i)(12 - 2i)
Answers
Answer:
[tex]2(-36 - 3i) +(5 +2i)(12 - 2i) \\ \implies - 72 - 6i + 60 - 10i + 24i + 4\\ \implies \: - 8 + 8i[/tex]
Related Questions
The slope of the line containing the points (-5, 3) and (-2, 1) is ________.
Answers
Answer:
-2/3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 1-3)/(-2 - -5)
= (1-3)/(-2+5)
= -2/3
Amit makes a cuboid having sides 3cm, 2cm & 3cm. How many such cuboids will be required to form a cube.
Answers
Start with a volume of a cuboid,
[tex]V=abc=3\cdot2\cdot3=18\mathrm{cm^3}[/tex]
The side of the cube we need equals to the LCM of the cubiod's sides,
[tex]\mathrm{LCM}(a,b,c)=\mathrm{LCM}(3,2,3)=6[/tex]
Now compute the volume of such cube,
[tex]V=\mathrm{LCM}(a,b,c)^3=6^3=216\mathrm{cm^3}[/tex]
Divide the volumes to get how many cubiods are in such cube,
[tex]\dfrac{V_{\mathrm{cube}}}{V_{\mathrm{cubiod}}}=\dfrac{216}{18}=\boxed{12}[/tex]
Hope this helps :)
Answer:
Hi,
Answer: 12
Step-by-step explanation:
lcm(3,2,3)=6
Volume of a cuboid=3*2*3=18 (cm³)
Volume of the cube=6³=216 (cm³)
Number of cuboids=216/18=12.
.80 to the 8th power
Answers
Answer:
0.16777216
Step-by-step explanation:
(. 8)^8=0.16777216
The 100 members of an extracurricular club at a nearby college are subdivided into 6
groups based on ethnic identification. Since 40% of the club is Caucasian, the
researcher ensures that 40% of his sample is also Caucasian. The researcher is using_____sampling
sampling.
A.random
B.cluster
C.stratified
D.systematic
Answers
Explanation:
Stratified sampling involves breaking a population of people into separate groups, where there isn't any overlap.
An example would be having a high school with freshmen, sophomores, juniors and seniors. A person can only belong to one group (so we can't have someone whos a freshman and a sophomore at the same time for instance). In that example, each group or strata is a different grade level.
As for this particular problem, each strata is a different ethnicity, and there are 6 strata total.
The researcher is using stratified sampling. The correct option is C.
What is stratified sampling?A method of sampling from a population that can be divided into subpopulations is known as stratified sampling in statistics. When subpopulations within a larger population differ, it may be desirable to sample each subpopulation separately in statistical surveys.
Stratified sampling involves breaking a population of people into separate groups, where there isn't any overlap.
An example would be having a high school with freshmen, sophomores, juniors, and seniors. A person can only belong to one group (so we can't have someone whos a freshman and a sophomore at the same time for instance). In that example, each group or strata is a different grade level.
As for this particular problem, each stratum is different ethnicity, and there is 6 strata total.
To know more about stratified sampling follow
https://brainly.com/question/1954758
#SPJ5
A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 400 randomly selected people who rode a jet ski, 86.5% wore life vests. Out of 250 randomly selected boaters, 92.8% wore life vests. Using a 0.10 level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2.
Step 2 of 3:
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2H0: p1=p2Ha: p1_p2
Step 3 of 3:
Draw a conclusion and interpret the decision.
Compute the value of the test statistic. Round your answer to two decimal places.
Answers
From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic, and use this to reach a conclusion.
This is a two-sample test, thus, it is needed to understand the central limit theorem and subtraction of normal variables.
Doing this:
The null hypothesis is [tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]The alternative hypothesis is [tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]The value of the test statistic is z = -2.67.The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.-------------------
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
-------------------------------------
Proportion 1: Jet-ski users
86.5% out of 400, thus:
[tex]p_1 = 0.865[/tex]
[tex]s_1 = \sqrt{\frac{0.865*0.135}{400}} = 0.0171[/tex]
Proportion 2: boaters
92.8% out of 250, so:
[tex]p_2 = 0.928[/tex]
[tex]s_2 = \sqrt{\frac{0.928*0.072}{250}} = 0.0163[/tex]
------------------------------------------------
Hypothesis:
Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
At the null hypothesis, it is tested that the proportions are the same, that is, the subtraction is 0. So
[tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]
At the alternative hypothesis, it is tested that the proportions are different, that is, the subtraction is different of 0. So
[tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]
------------------------------------------------------
Test statistic:
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis.
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_1 - p_2 = 0.865 - 0.928 = -0.063[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0171^2 + 0.0163^2} = 0.0236[/tex]
The value of the test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.063 - 0}{0.0236}[/tex]
[tex]z = -2.67[/tex]
The value of the test statistic is z = -2.67.
---------------------------------------------
p-value of the test and decision:
The p-value of the test is the probability that the proportion differs by at at least 0.063, which is P(|z| > 2.67), given by 2 multiplied by the p-value of z = -2.67.
Looking at the z-table, z = -2.67 has a p-value of 0.0038.
2*0.0038 = 0.0076.
The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
A similar question is found at https://brainly.com/question/24250158
Does the equation, x + y = 6 show direct variation?
Answers
Answer:
Yeah, x varies directly with (6 - y)
Step-by-step explanation:
[tex]x = 6 - y \\ x = k(6 - y) \\ x \: \alpha \: (6 - y)[/tex]
I need help on this 20 points
Answers
Answer:
4^15
Step-by-step explanation:
We know a^b^c = a^(b*c)
4^3^5
4^(3*5)
4^15
Help me pls ASAP I WILL GIVE BRAINLIEST
-3 = -e/75
Answers
9514 1404 393
Answer:
e = 225
Step-by-step explanation:
To eliminate the coefficient of e, multiply both sides of the equation by its reciprocal. The reciprocal of -1/75 is -75.
(-75)(-3) = (-75)(-e/75)
225 = e
Robert owns two dogs. Each day, one dog eats
1/6 of a scoop of dog food and the other dog eats br
1/6 of a scoop. Together, how much dog food do
the two dogs eat each day? Write in simplest
form.
Answers
Answer:
2/3 scoop
Step-by-step explanation:
1/6 + 1/6 = 2/6 = 1/3
Answer: 2/3 scoop
what is the volume of the solid?
Answers
9514 1404 393
Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
__
The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
__
The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
which function defins (g-f) (x)
Answers
Answer:
(g÷f) (x) (1.8) ³x²+⁷x+2
Step-by-step explanation:
Im glad to help you
Mr Makgato sells his car for R42 000.00. The total commission is 7.2% of the selling price of which the broker receives 2 thirds and the salesperson receives the rest. How much does the broker receive?
Answers
Answer:
2016
Step-by-step explanation:
using USA dollars:
$42000 x .072 (7.2%) = 3024 total commission
3024 x 2/3 = 2016 brokers amount
find the value of x, circles and angles
Answers
Answer:
x = 50
Step-by-step explanation:
When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:
[tex]\frac{x+96}{2} = 73[/tex]
x + 96 = 146
x = 50
A study was conducted in order to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.
A similar study conducted a year earlier estimated that ?, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
a. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
b. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
c. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
e. None of the above. The only way to reach a conclusion is by finding the p-value of the test.
Answers
Answer:
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
Step-by-step explanation:
Mean was of 8 hours, test if it has changed:
At the null hypothesis, we test if it has not changed, that is, the mean is still of 8, so:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if it has changed, that is, the mean is different of 8, so:
[tex]H_1: \mu \neq 8[/tex]
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
8 is part of the confidence interval, which means that the study does not provide evidence that the mean has changed, and the correct answer is given by option d.
find the angle vector of 7j +10 k,i +6j+6k,-4i+9j+6k
Answers
Answer:
Right angled and isosceles
help with 30 please. thanks.
Answers
Answer:
See Below.
Step-by-step explanation:
We have the equation:
[tex]\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}[/tex]
And we want to show that:
[tex]\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}[/tex]
Instead of differentiating directly, we can first square both sides:
[tex]\displaystyle y^2 = 3e^{2x} -4x + 1[/tex]
We can find the first derivative through implicit differentiation:
[tex]\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4[/tex]
Hence:
[tex]\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}[/tex]
And we can find the second derivative by using the quotient rule:
[tex]\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}[/tex]
Substitute:
[tex]\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}[/tex]
Simplify:
[tex]\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}[/tex]
Combine fractions:
[tex]\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}[/tex]
Simplify:
[tex]\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}[/tex]
Simplify:
[tex]6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}[/tex]
Q.E.D.
Three research departments have 6, 9,
and 7 members, respectively. Each
department is to select a delegate
and an alternate to represent the
department at a conference. In how
many ways can this be done?
Answers
Answer:
I don't know because I don't understand what you mean
Find the value of z.
54°
X
2049
(32+1)°
A. 25.25
OB. 129
Answers
Answer:
Step-by-step explanation:
(z)° + (3z + 1)° = 360° - ( 54° + 204° )
z + 3z + 1 = 360 - 258
4z = 101
z = 25.25
A gift box shown below is packed with small cubic 1/2 inch blocks. The blocks are packed tightly with no spaces between them.
A. How many blocks are in the gift box?
B. What is the volume of the gift box?
C. Find how much wrapping paper will be needed to wrap the gift box (hint: find surface area).
Answers
Step-by-step explanation:
the box is
9 in × 3.5 in × 4.5 in = 141.75 in³
each block is
0.5 in × 0.5 in × 0.5 in = 0.125 in³ (1/8 in³)
so, we can fit
141.75 / 0.125 = 1134
blocks into the box.
and they fit neatly, as the dimensions of the box and the cubes allow a tight packing without any empty left over space in the box.
Can some help with the answer please it’s very much needed and apprIeciated
Answers
Answer:
A
Step-by-step explanation:
The degree of the Polynomial is 3
Consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide . If a preliminary data indicate a standard deviation of 20g . What sample of adults should be selected for the study?
Answers
Answer:
With an ageing population, dietary approaches to promote health and independence later in life are needed. In part, this can be achieved by maintaining muscle mass and strength as people age. New evidence suggests that current dietary recommendations for protein intake may be insufficient to achieve this goal and that individuals might benefit by increasing their intake and frequency of consumption of high-quality protein. However, the environmental effects of increasing animal-protein production are a concern, and alternative, more sustainable protein sources should be considered. Protein is known to be more satiating than other macronutrients, and it is unclear whether diets high in plant proteins affect the appetite of older adults as they should be recommended for individuals at risk of malnutrition. The review considers the protein needs of an ageing population (>40 years old), sustainable protein sources, appetite-related implications of diets high in plant proteins, and related areas for future research.
A company's prime costs total $4,572,000 and its conversion costs total $5,580,000. If direct materials costs are $2,088,000, calculate the overhead costs
Answers
Answer:
dont know
Step-by-step explanation:
Find the value of x.
Answers
the tic marks show that all sides are congruent, same with the angles. 60+60+60=180 also.
PLEASE HELP ME
An expression is shown below:
6x^2y − 3xy − 24xy^2 + 12y^2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Answers
9514 1404 393
Answer:
(3y)(2x^2 -1x -8xy +4y)(3y)(x -4y)(2x -1)Step-by-step explanation:
Part A: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...
(3y)(2x^2 -1x -8xy +4y)
__
Part B: The remaining factor can be factored pairwise:
3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)
resolver utilizando la regla de clamer
Answers
Answer:
pordondede donde eres?
Step-by-step explanation:
........................
caron makes $6 every 30 minutes. using the double number line diagram below, how much money would she make if she worked 80 minutes at the same rate?
Answers
Answer:
$16
Step-by-step explanation:
Both lines start at 0 and at 30 mins it is $6. It displays a ratio so that means every 10 mins they earn $2
9. What is m JKM? A 28° C 90° B 58.5° D 117°
Answers
Step-by-step explanation:
her it Go i think it is helpful for u
Find the nominal rate jm equivalent to the annual effective rate j, if (a) j= 6%, m = 2; (b) j = 9%, m = 4; (c) j = 10%, m = 12; (d) j = 17%, m = 365; (e)j = 8%, m = 52; j = 11.82%, m = 00. Ans. (a) 5.91%; (b6) 8.71%; (e) 9.57%; (d) 15.70%; (e) 7.70%:
A consumer buys goods worth $1500, paying $500 down and $500 at the end of 6 months. If the store charges interest at j1a = 18% on the final payment will be necessary at the end of one year?
Answers
The graph shown is the solution set for which of the following inequalities?
Answers
Answer:
b is your answer hope it is helpful
Answer:
b is the correct answer
Step-by-step explanation:
the answer is b
The three-dimensional shape that this net represents is a _?
The surface area of the figure is _?
square centimeters.
Answers
Answer:
Step-by-step explanation:
It’s a cube with edge length of 12 cm.
The cube has six faces, and the are ma if each face is 144 cm²
Total surface area = 6×144 = 864 cm²
Answer:
cube 864
Step-by-step explanation:
